This extension is needed for, among other things, modeling the concepts of " is an element of " or " is a subset of " in set theory, without running into logical inconsistencies such as Russell's paradox.

However, as this article is examining preorders as a logical extension of non-strict partial orders, the current definition is more intuitive.

Punctuated equilibrium originated as a logical extension of Ernst Mayr's concept of genetic revolutions by allopatric and especially peripatric speciation as applied to the fossil record.

However, some authors ( including mathematicians ) use φ for inclination ( or elevation ) and θ for azimuth, which " provides a logical extension of the usual polar coordinates notation ".

Kaplan maintained that the War of 1812 was the logical extension of his embargo and that, by entering the Napoleonic Wars on anti-British side, the United States gave up the advantages of neutrality.

During this same post-war period, with the aim of further delegitimizing war as an acceptable and logical extension of foreign policy, most national governments also renamed their Ministries or Departments of War as their Ministries or Departments of Defense, for example, the former US Department of War was renamed as the US Department of Defense.

This was a logical extension of his boundless faith in the rule of law as a Progressive, and it therefore even superseded U. S nationalism as embodied in the Constitution.

So the extension of " Lassie is famous " is the logical value ' true ', since Lassie ' is ' famous.

According to Mattias Gardell, NSBM musicians see " national socialism as a logical extension of the political and spiritual dissidence inherent in black metal ".

“ Radiant Systems is a logical and strategic extension for NCR, moving us into attractive fast-growth adjacent markets ,” Bill Nuti, NCR ’ s chairman and chief executive, said in a statement.

Systems based on functional languages such as Lisp hence need to include a subsystem for the representation of logical assertions, while logic oriented systems such as those using the language Prolog generally rely on an extension of the built in logical representation framework.

Verbal Behavior is the logical extension of Skinner's ideas, in which he introduced new functional relationship categories such as intraverbals, Autoclitics, mands, tacts and the controlling relationship of the audience.

More recent scholars however have posited that the formation of the themes did not constitute a radical break with the past, but rather a logical extension of pre-existing, 6th-century trends, and that its direct social impact was minimal.

For instance, a game might define a logical relationship between a knight and a horse so that the knight is considered an extension to the horse.

Kwame Nkrumah, president of Ghana ( 1960 – 66 ), coined the term neo-colonialism in the book Neo-Colonialism, the Last Stage of Imperialism ( 1965 ) As a political scientist, Nkrumah theoretically developed and extended, to the post – War 20th century, the socio-economic and political arguments presented by Lenin in the pamphlet Imperialism, the Highest Stage of Capitalism ( 1917 ), about 19th-century imperialism as the logical extension of geopolitical power to meet the financial investment needs of the political economy of capitalism.

Their invention of corn flakes was a logical extension of the Grahamite approach to nutrition.

According to a well known architecture critic, the new extension had three main tasks: " how to dock amicably with the existing architecture ; how to provide the resulting whole with a new street ' address '; how to create a logical, legible and deferential hanging space for the collection.

By extension, handwaving is used in speculative fiction criticism to refer to a plot device ( e. g., a scientific discovery, a political development, or rules governing the behavior of a fictional creature ) that is left unexplained or sloppily explained because it is convenient to the story, with the implication that the writer is aware of the logical weakness but hopes the reader will not notice or will suspend disbelief.

Hypermedia is used as a logical extension of the term hypertext in which graphics, audio, video, plain text and hyperlinks intertwine to create a generally non-linear medium of information.

The concept was invented by the self-declared World Citizen Garry Davis in 1949, as a logical extension of the idea of individuals declaring themselves world citizens, and promoted by Robert Sarrazac, a former leader of the French Résistance who created the Human Front of World Citizens in 1945.

The Saguna school was represented by mainly Vaishnava poets like Surdas, Tulsidas and others and was a logical extension of the Dvaita and Vishishta Advaita Philosophy propounded by the likes of Madhavacharya etc.

These attempts were basically an extension of his earlier thoughts in the philosophy of mathematics, for example his 1810 Beiträge where he emphasized the distinction between the objective relationship between logical consequences and our subjective recognition of these connections.

Whilst one may regard functionalism as a logical extension of the organic analogies for society presented by political philosophers such as Rousseau, sociology draws firmer attention to those institutions unique to industrialised capitalist society ( or modernity ).

It soon became clear to many of those involved in PET development that a circular or cylindrical array of detectors was the logical next step in PET instrumentation.

After all, Woodruff owned a competent printing plant and was the logical man for the job.

It was logical that he would come up with the figure of the modern jazz musician.

It was a succession of picture-images passing through his mind: the same ones, different ones, in no apparent sequence, in no logical succession.

Skorich was considered the logical choice after the club gave Norm Van Brocklin permission to seek the head coaching job with the Minnesota Vikings, the newest National Football League entry.

The fact is incontestable: that liberal world of Unitarian Boston was narrow-minded, intellectually sterile, smug, afraid of the logical consequences of its own mild ventures into iconoclasm, and quite prepared to resort to hysterical repressions when its brittle foundations were threatened.

And though it was logical that a man who could plot mass murder would not hesitate to speak an untruth, still it was difficult to understand why Spencer spoke only for Cromwell.

This was not, for the Angel, just a matter of running through a logical or deductive chain, or deciding on some action from some already established premise.

He was essentially a theorist, and his great merit lay in the capacity of taking over experimental work that others had carried out — without always adequately recognizing their claims — and by a rigorous logical procedure, reinforced by his own quantitative experiments, of expounding the true explanation of the results.

Since the bigger 1 / 4 " tapioca pearls are separately sold as " black pearls " ( 黑珍珠 ) in markets, this name was the logical first choice and is more popular with the consumers of the drink.

This was a logical continuation to Birka's position as the first missionary town in Sweden.

As early as 1886 he saw that logical operations could be carried out by electrical switching circuits ; the same idea as was used decades later to produce digital computers.

For a twentieth century thinker committed to the same ideal, government was an essential tool to the same end ... odern liberalism is instead the logical and sociological outcome of classical liberalism.

He said he wanted to confront the Americans " with more than words ... the logical answer was missiles ".

Pissarro explained the new art form as a “ phase in the logical march of Impressionism ”, but he was alone among the other Impressionists with this attitude, however.

For compatibility and ease of implementation, the 1571's double-sided format of one logical disk side with 70 tracks was created by putting together the lower 35 physical tracks on each of the physical sides of the disk rather than using two times 40 tracks, even though there were no more quality problems with the mechanisms of the 1571 drives.

Until recently, Hume was seen as a forerunner of the logical positivist movement ; a form of anti-metaphysical empiricism.

According to the logical positivists, unless a statement could be verified by experience, or else was true or false by definition ( i. e. either tautological or contradictory ), then it was meaningless ( this is a summary statement of their verification principle ).

This focus on meta-ethics was in part caused by an intense linguistic focus in analytic philosophy and by the popularity of logical positivism.

Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.

The work of both authors was heavily influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers ( a Gödel numbering ) to logical formulas in order to reduce logic to arithmetic.

Louis was a weak and ineffectual military leader with no skill for maintaining troop discipline or morale, or of making informed and logical tactical decisions.

Clemence ( 1948 ) made it clear that his proposal was intended " for the convenience of astronomers and other scientists only " and that it was " logical to continue the use of mean solar time for civil purposes ".